To determine factor pairs you can make an iterative loop, and check for how many times your input value is evenly divided by a number, ie. for 6 you would check:

6 % 1 = 0, 6 % 2 = 0, 6 % 3 = 0, 6 % 4 = 2, 6 % 5 = 1, 6 % 6 = 0

There are 4 zeros, so 6 has 4 factors.

Determining factor pairs takes a little bit more work than you would imagine, as you cannot simply divide by 2, because of square numbers, who have an odd number of factors.

Instead, you can ignore 1 as a factor, divide the amount of other factors by 2, then add 1 to your amount of factor pairs.

This process may look like:

int i;
for (i=2; i<=input; i++) {
    if ((input % i) == 0) {
    factorpairs++;
    }
}
factorpairs = (factorpairs / 2) + 1

A for loop is a loop that iterates based on a set of given parameters for example a for loop that starts at 0 and iterates 1000 times would look like:

int i;
for (i=0; i<=1000; i++) {
    whatever you want to happen;
} 

A while loop is a loop that continues to iterate as long as the input evaluates to true. a while loop that iterates until an input variable reaches some designated value may look like:

while (var != 100) {
    whatever you want it to do;
    }

If you arent careful with your condition a while loop will iterate endlessly, preventing your code from moving past the loop

unsigned int var = 0;
var = 20;
while (var == 20){
    do something that doesnt effect var;
    }
the rest of your code;

In this case, because var never changes from 20, the while loop will never end You can also achieve this endless iteration by typing

 while (true) {
    some code;
    }

Because the condition is always true it will never escape the loop